$g(t) = 7t+5-2(h(t))$ $f(t) = 4t^{2}+6t-5-5(h(t))$ $h(x) = 4x$ $ f(g(3)) = {?} $
First, let's solve for the value of the inner function, $g(3)$ . Then we'll know what to plug into the outer function. $g(3) = (7)(3)+5-2(h(3))$ To solve for the value of $g$ , we need to solve for the value of $h(3)$ $h(3) = (4)(3)$ $h(3) = 12$ That means $g(3) = (7)(3)+5+(-2)(12)$ $g(3) = 2$ Now we know that $g(3) = 2$ . Let's solve for $f(g(3))$ , which is $f(2)$ $f(2) = 4(2^{2})+(6)(2)-5-5(h(2))$ To solve for the value of $f$ , we need to solve for the value of $h(2)$ $h(2) = (4)(2)$ $h(2) = 8$ That means $f(2) = 4(2^{2})+(6)(2)-5+(-5)(8)$ $f(2) = -17$